Thanks to dedicated X-ray monitoring observations of the Galactic bulge with the Wide Field Cameras on BeppoSAX, several tens of faint X-ray transients have been discovered with peak fluxes that are just a few percent of that of classical X-ray novae. Most of these faint transients exhibit type-I X-ray bursts and, thus, harbor a neutron star. A few cases do not, like SAX J1711.6-3808 which was active between January and May 2001. We followed up this transient with BeppoSAX, RXTE and XMM-Newton. The 1-200 keV spectrum is characterized by Comptonization, a transient soft excess and a 2.6 keV (FWHM) broad emission feature at the Fe-K line complex whose flux peaks in tandem with that of the soft excess. The emission feature is reminiscent to that seen in the classical black hole candidate Cyg X-1. We propose that SAX J1711.6-3808 contains a black hole, and that the broadness of the emission feature is related to Doppler shifts due to orbital motion of the emitting material around the compact object. This would be the 4th time that a broad Fe-K emission feature has been detected in a Galactic black hole.